On the effect of van Hove singularities on the critical current of high-T-c junctions

We show that the Josephson critical current between two 2-dimensional super conductors can be strongly affected by the Van Hove singularity of the dens ity of states characteristic of 2-dimensional metals. In particular, when t he Fermi level falls at the singularity, the critical current is zero for c ertain crystallographic misorientations between the two superconductors. Th is effect sems to have been observed recently in high-T-c grain boundary ju nction experiments.